If the backyard_house isn't in range of the router then chances are the repeater wouldn't be in range either.
Just an idea, you could wire another access point in your main house (we'll call this AP2). Use one with a directional antenna and put it in a location within the main house that is closest to the backyard_house. Preferably at a window.
Then add a repeater to the backyard_house. Face the AP2 directional antenna directly at the repeater. Then backyard_house devices can be connected to the repeater for network access.